C++ Neural Networks and Fuzzy Logic: Preface

Figure 5.4

  The step function.

Note:  You can think of a sigmoid function as a fuzzy step function.

The Ramp Function

To describe the ramp function simply, first consider a step function that makes a jump from 0 to 1 at some

point. Instead of letting it take a sudden jump like that at one point, let it gradually gain in value, along a

straight line (looks like a ramp), over a finite interval reaching from an initial 0 to a final 1. Thus, you get a

ramp function. You can think of a ramp function as a piecewise linear approximation of a sigmoid. The

graph of a ramp function is illustrated in Figure 5.5.

Figure 5.5

  Graph of a ramp function.

Linear Function

A linear function is a simple one given by an equation of the form:

f(x) = ±x + ²

When ± = 1, the application of this threshold function amounts to simply adding a bias equal to ² to the sum

of the inputs.

C++ Neural Networks and Fuzzy Logic:Preface

The Step Function

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Applications

As briefly indicated before, the areas of application generally include auto− and heteroassociation, pattern

recognition, data compression, data completion, signal filtering, image processing, forecasting, handwriting

recognition, and optimization. The type of connections in the network, and the type of learning algorithm used

must be chosen appropriate to the application. For example, a network with lateral connections can do

autoassociation, while a feed−forward type can do forecasting.